Question

27. A police jeep is chasing with speed of 30 m/s
towards a thief going far with speed 180 km/h.
Police fires a bullet with muzzle speed of 120
m/s. By what speed bullet strikes the thief?
(1) 70 m/s
(2) 150 m/s
(3) 120 m/s
(4) 100 m/s​

Answer 1

Answer:

100 m/s

Explanation:

A police jeep is chasing with speed of 30 m/s

towards a thief going far with speed 180 km/h.

Police fires a bullet with muzzle speed of 120

m/s. By what speed bullet strikes the thief?

Speed of bullet =  muzzle speed + Vehicle speed

=> Speed of bullet = 120 + 30 = 150 m/s

Speed of thief = 180 km/Hr = 180 * 1000/3600  = 50 m/s

Speed by which bullet strikes = Speed of bullet - Speed of thief

=> Speed by which bullet strikes = 150 - 50 = 100m/s

bullet strikes the thief with 100 m/s

Answer 2

answer : option (4) 100m/s

explanation : speed of police jeep, $u_j$ = 30m/s

speed of bullet with respect to police jeep is fired with muzzle , $v_{bj}$ = 120m/s

so, speed of bullet will be ; $v_{bj}= v_b-v_j$

or, 120m/s = $v_b$ - 30m/s

or, $v_b$ = 120m/s + 30m/s = 150m/s

hence, velocity of bullet with respect to ground, $v_b$ = 150m/s

speed of thief with respect to ground , $v_t$ = 180km/h

= 180 × 1000m/(3600s)

= 180 × 5/18 m/s

= 50m/s

now, velocity of bullet with respect to thief = velocity of bullet with respect to ground - velocity of theif with respect to ground.

i.e., $v_{bt}=v_b-v_t$

= 150m/s - 50m/s

= 100m/s

so, speed of bullet by which it strikes the thief is 100m/s